1. Field of the Invention
The present invention relates to a probability density function separating apparatus, a probability density function separating method, a noise separating apparatus, a noise separating method, a testing apparatus, a testing method, a calculating apparatus, a calculating method, a program, and a recording medium. More particularly, the present invention relates to an apparatus and a method for separating a deterministic component and a random component from a probability density function.
2. Related Art
A method for separating a probability density function with a deterministic component and a probability density function with a random jitter component can be used in an oscilloscope, a time interval analyzer, a universal time frequency counter, automated test equipment, a spectrum analyzer, a network analyzer, and so on. A signal under measurement may be an electrical signal or an optical signal.
When amplitude of the signal under measurement is degraded, a probability by which a reception bit one is erroneously decided to a bit zero is increased. Similarly, when a timing of the signal under measurement is degraded, a probability of an erroneous decision is increased in proportion to the degradation. It takes longer observation time than Tb/Pe to measure these bit error rates Pe (however, Tb shows a bit rate). As a result, it takes long measurement time to measure an extremely small bit error rate.
For this reason, as measures against amplitude degradation, there has been used a method for setting a bit decision threshold value to a comparatively large value to measure a bit error rate and extrapolate it into an area with an extremely small bit error rate. A deterministic component of a probability density function is bounded and causes a bounded bit error rate. On the other hand, a random component of a probability density function is unbounded. Therefore, a technique for accurately separating a deterministic component and a random component included in measured probability density function and causing bit error rate becomes important.
Conventionally, as a method for separating a deterministic component and a random component included in a probability density function or the like, for example, the invention disclosed in US 2002/0120420 has been known. According to this method, an estimate of variance of a probability density function over a predetermined the interval is computed and the computed estimate of variance is transformed into a frequency domain, in order to determine a random component and a period component constituting the variance. The method uses changing a measured time interval from one cycle to N cycles to measure an autocorrelation function of a period component and an autocorrelation function of a random component and making the Fourier transform respectively correspond to a line spectrum and a white noise spectrum. Here, the variance is a sum of a correlation coefficient of a period component and a correlation coefficient of a random component.
However, a probability density function is given by convolution integrating a deterministic component and a random component. Therefore, according to this method, it is not possible to separate a deterministic component and a random component from a probability density function.
Moreover, as another method for separating a deterministic component and a random component included in a probability density function or the like, for example, the invention disclosed in US2005/0027477 has been known. As shown in FIG. 2 to be described below, according to this method, both tails of a probability density function are fitted to Gaussian distribution in order to separate two random components from the probability density function. In this method, random components and a deterministic component are performed fit of Gaussian curves under the assumption that both components do not interfere with each other, in order to separate a random component corresponding to Gaussian distribution.
However, it is generally difficult to uniquely determine a boundary between a random component and a deterministic component, and it is difficult to separate a random component with high precision in this method. Moreover, as shown in FIG. 2 to be described below, according to this method, a deterministic component is computed based on a difference D(δδ) between two time instants corresponding to a mean value of each random component.
However, for example, when a deterministic component is a sine wave or the like, it is experimentally confirmed that this difference D(δδ) shows a smaller value than D(p-p) of a true value. In other words, according to this method, since only an ideal deterministic component by a square wave can be approximated, various deterministic components such as a deterministic component of a sine wave are not measured. Furthermore, a measurement error of a random component is also large.
Moreover, about a probability density function of which a plurality of deterministic components are convolution integrated, a method by which each component can be separated from the function does not exist.